Answer:
No
Step-by-step explanation:
Assume you are asking if 30 in, 30 in, 25 in triangle if right.
Since two longer sides are equal this can't be a right triangle. Remember the hypotenuse is the longest side and the right triangle can be isosceles if shorter sides are of same size.
Check through Pythagorean theorem
H²=P²+B²301²=30²+25²No it's false
It's not right angled
(Figure 1) shows a history graph at x = 0 m of a wave moving to the right at 1 m/s. What is the snapshot graph of this wave at t = 0 s ?
The snapshot graph of this wave at t = 0 s is the mirror image about y-axis. So, option B is correct.
What is meant by graph?An illustration of a relation is a function graph. In set theory and modern mathematical foundations, a function is truly equal to its graph.
An illustration of a relation is a function graph. In set theory and modern mathematical foundations, a function is truly equal to its graph. It is often helpful to think about functions as mappings, which include the sets that constitute the domain and the codomain in addition to the relationship between input and output. A codomain should be considered, for instance, while determining if a function is onto (surjective) or not. The codomain is not determined by the graph of a function alone. The terms "function" and "graph of a function" are frequently used[3] because, although they refer to the same thing, they convey a different viewpoint.
The equation of forward travelling wave is :
P(x, t)=g(x-vt)
Here, v=1m/s
P(x, t)=g(x-t)
At x=0,
P(0, t)=g(-t) ------(1)
But at t=0,
P(x, 0)=g(x) -------(2)
From the equations 1 and 2,
You can see that R.H.S of both port are just the mirror image about y-axis
So, option B is correct.
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Suppose the population of a certain state is 6,215,000. If 435,050 are children under 5 years of age, 4,972,00 are between the ages of 5 and 65, and 807,950 are over 65, what percentage of people make up each age group?
(A) under 5: ___
(B) between 5 and 65: ___
(C) over 65: ___
Answer:
A) 435,050/6,215,000= 0.07= 7%
B) 4,972,000/6,215,000= 0.8= 80%
C) 6,215,000-(4,972,000+435,050)= 807,950
807,950/6,215,000=0.13=13%
The first steps in writing f(x) = 4x2 + 48x + 10 in vertex form are shown.
f(x) = 4(x2 + 12x) + 10
(twelve-halves) squared = 36
What is the function written in vertex form?
f(x) = 4(x + 6)2 + 10
f(x) = 4(x + 6)2 – 26
f(x) = 4(x + 6)2 – 134
f(x) = 4(x + 6)2 + 154
The function written in vertex form is:
f(x) = 4(x + 6)² - 26
Option B is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = 4(x² + 12x) + 10
Now,
f(x) = 4(x² + 12x) + 10
f(x) = 4 (x² + 2 x (x) x 6 + 36) - 36 + 10
f(x) = 4(x + 6)² - 26
Thus,
f(x) = 4(x + 6)² - 26 is the function in vertex form.
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Answer:
B is correct
Step-by-step explanation:
Plz help me answer this question
Answer:
Line A
Step-by-step explanation:
If the sequence 2, 4, 6, 10, 16, ... were to follow the same pattern as the Fibonacci sequence, what are the next three terms?
A. 18, 22, 24
B. 26, 30, 36
C. 26, 42, 68
D. 26, 42, 66
Answer:
10 + 16 = 26
16 + 26 = 42
26 + 42 = 68
(C) the next three terms are 26, 42, 68
Which similarity postulate or theorem can be used to verify that the two
triangles shown below are similar?
A. SAS theorem
B. SSS theorem
C. AA postulate
D. Similarity cannot be determined.
Answer:
C
Step-by-step explanation:
AA postulate because we are given 2 of the 3 angles of each triangle. They are both the same in each triangle. Also, we can find the 3rd angle in each triangle. Since both triangles have the exact same angles, they are similar.
The given triangles ΔABC and ΔLMN are similar by AA postulate.
What is a triangle?A triangle is a three sided polygon that consist of three edges and three vertices .
Here two given triangles are ΔABC and ΔLMN. In these two triangles ∠A=∠L=53° and ∠B=∠M= 72°.
Therefore, the two corresponding angles of triangles ΔABC and ΔLMN are equal . So the third angle of ΔABC is also equal to the corresponding angle of ΔLMN.
Hence two triangles are similar by AA postulate.
Thus two triangles are similar by AA postulate. So option (C) is correct.
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A rectangular driveway is 7 feet wide, and it has an area of a square feet. How long is the driveway?
Please give how to solve every step
☆ Thank you ☆
Answer:
x = a/7
Step-by-step explanation:
Area is length x width, so let's call our unknown, the length, x
So the total area is 7 (the width) times x
If the total area is a, then we can write the equation a = 7(x)
Next, we have to isolate the variable for the length, x
To do this, we divide both sides by 7, leaving a/7 = x, or x = a/7
where is alrquan07 ? Anyone know?
Answer:
hewo friend
Step-by-step explanation:
2. What is the x-coordinate of the image of point (2,-5) after reflection in the
line y=x?
The X coordinate of the image is (-5,2)
What is meant by coordinate ?A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).
The coordinates of one point in the coordinate system are included in an ordered pair. An ordered pair of the form of a point's name is (x, y). The x-coordinate is represented by the first integer, and the y-coordinate by the second. You must place a dot at the coordinates of the ordered pair in order to graph a point.
Given
The coordinates for x and y change when you consider the line y=x. The end product is (-5,2)
Because (-5,2) its reflection means x coordinate will y coordinate and y coordinate will x coordinate so the coordinate be (-5,2)
The complete question is : Find the coordinates of the image of point (2,-5) after a reflection in the line y=x
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{[(66/11) + 3 ] x2}
PLEASE HELPP
Answer:
((66/11)+)x2
(6)+3)x2
18+2
=20
Step-by-step explanation:
you can divide and copy the 2 and 3 and you times the 6x3 copy 2 then plus thats the equal of 20..
I HOPE ITS HELP THANK YOU
A 21-foot beam is to be cut into three pieces so that the second and third piece are each 3 times the length of the first piece. If X represents represents the length of the first piece find the length of each piece.
The length of the first piece is 3 inches, and the second and third pieces are each 9 inches
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
Given that a 21-foot beam is to be cut into three pieces so that the second and third pieces are each 3 times the length of the first piece.
We have to determine the length of each piece.
Let x represents the length of the first piece
As per the given condition,
x + 3x + 3x = 21
7x = 21
x = 21 / 7
x = 3
Thus, the first piece is 3 inch
So 2nd piece is 3×3 = 9 inches ( 3 times to first piece )
And 3rd piece is 3×3 = 9 inches ( 3 times to first piece )
Therefore, the length of the first piece is 3 inches, and the second and third pieces are each 9 inches
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please help!! i need to know very soon!
Answer:
about 46
Step-by-step explanation:
WZ and XR are diameters. Find the measure of arc ZWX. (The figure is not drawn to scale. )
The measure of arc ZWX is 180 degrees.
Given that WZ and XR are diameters, we know that they are both perpendicular to chord WX. This creates four right angles at point X, and as a result, we have a rectangle formed by the four line segments.
Since WZ and XR are diameters, they each extend from one end of the rectangle to the other. This means that arc ZWX is actually a semicircle, with a measure of 180 degrees.
To see why this is the case, consider that a full circle has a measure of 360 degrees. Since arc ZWX spans exactly half of the circle, it must have a measure of half the circle, or 180 degrees.
In summary, the measure of arc ZWX is 180 degrees. This can be derived from the fact that WZ and XR are diameters, which create a rectangle and a semicircle in the process. While the figure may not be drawn to scale, the relationships between the different line segments and angles remain constant, allowing us to determine the measure of arc ZWX with confidence.
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a bin contains 5 red balls and 9 blue balls. the following experiment is repeated several times: remove a ball from the bin, observe its color, and replace it. what is the probability that the 5th ball drawn is red and the 8th ball drawn is blue?
The probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.
What is probability ?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
The probability of drawing a red ball on the 5th draw is the number of red balls divided by the total number of balls in the bin, which is 5/14. The probability of drawing a blue ball on the 8th draw is the number of blue balls divided by the total number of balls in the bin, which is 9/14.
The probability of both events happening is the product of the individual probabilities:
P(red on 5th draw and blue on 8th draw) = (5/14) * (9/14) = 45/196
So, the probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.
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The probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
The probability of drawing a red ball on the 5th draw is the number of red balls divided by the total number of balls in the bin, which is 5/14. The probability of drawing a blue ball on the 8th draw is the number of blue balls divided by the total number of balls in the bin, which is 9/14.
The probability of both events happening is the product of the individual probabilities:
P(red on 5th draw and blue on 8th draw) = (5/14) * (9/14) = 45/196
So, the probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.
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Maddi needs to rent a car.the rental costs$13 per hour Plus a processing fee of 100$. Which is the independent variable costs or time.
Answer:
The independent variable is time.
Step-by-step explanation:
(Y=mx+b format)
Maddi's rental for the car costs $13 per hour so the x variable would be the hours (x=hour). This would be a Y= mx + b equation and in this case, Y=13x + 100. Independent means (mathmatically) a variable that does not depend on any other variable for its value. The costs is always changing being dependent on the time portion. The time isn't dependent on anything. Thus, the independent variable is time.
(If you need a starting point which is b, it would be the $100 as the processing fee.)
Part A Write the multiplication expression shown by the model. Do not solve the problem.
help
The multiplication expressions shown by the model are:
Green squares: (4 x 10) + (1 x 6)Red squares: (4 + 2) + (4 x 10)Blue squares: (8 x 2) (3 x 10)Ash squares: (2 + (6 x 10)What are multiplication expressions?A multiplication expression is a mathematical statement that uses the multiplication operand with either number, variables, or a combination of the two to produce results.
The numbers or variables in a multiplication expression are known as multiplicand (the first number to be multiplied) and multiplier (the second number multiplying).
The result or solution of a multiplication operation is known as the product.
Thus, other possible multiplication expressions can be written out from the model because of the additive property of multiplication.
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If x≠4 and x≠-4, the fraction x^2-8x+16/x^2-16 can be simplified to what?
For the given fraction x^2-8x+16/x^2-16 if x≠4 and x≠-4 the simplified fraction is (x-4)/(x+4).
Simplified fraction refers to the fractions in their lowest form which has been reduced and simplified. The numerator and denominator in the fraction are reduced in simplified fraction to the extent that the only common factor between them is 1.
In order to simplify the fraction (x^2-8x+16)/(x^2-16), first, we must factor the numerator and denominator of the fraction:
Numerator: x^2-8x+16 = (x-4)(x-4) = (x-4)^2
Denominator: x^2-16 = (x-4)(x+4)
So the fraction becomes:
(x-4)^2/(x-4)(x+4)
Next, we can simplify the fraction by canceling out the (x-4) term in the numerator and denominator:
(x-4)/(x+4)
Therefore, the simplified fraction is (x-4)/(x+4) if x≠4 and x≠-4.
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7. The quadratic function below models the flight of a model rocket, where
the height, h(t) is in metres, and the time, t is in seconds. What is the
rocket's height after 3 seconds?
h(t) = -5t² +42t + 54
The rocket's height after 3 seconds is 6.3 sec.
The quadratic equation y = -x2 - 12x, where y is the height of the rocket in metres at time x seconds after launch, may be used to describe the trajectory of a model rocket. The rocket's highest point should be noted, along with the time it was at that height.
A rocket's height is a function of time, h(t), where h is measured in metres and t is measured in seconds. 9.8 m/s2 is the rate of change of velocity (d2h dt2 - t). The rocket is catapulted into the air, reaching a speed of 50 m/s at time t0.
To find the rocket's height at t = 2 sec, we just have to substitute 2 into the equation for t and then solve for h:
h = -5*t2 + 30*t + 10
h = -5(2)2 + 30(2) + 10
h = -5(4) + 30(2) + 10
h = -20 + 60 +10
h = 50 m
The height of the rocket 2 seconds after launching it is 50 meters.
To find the x-coordinate of the vertex of a parabola, we use the formula:
\(xvertex = -b / 2a\)
t - 3 = ± √(11)
t = 3 ± √(11)
t = 3 ± 3.3
Solving for t, we get two solutions:
t = 3 - 3.3
t = -0.3 sec
and
t = 3 + 3.3
t = 6.3 sec
Remember that the rocket takes off from an elevated platform (the roof of a building), not from the ground, in order to comprehend the two alternatives we came up with. Even though we have two x-intercepts, only one of them, tground = 6.3 seconds, is related to when the rocket touches down. The other x-intercept, t = -0.3 sec, only has theoretical significance and is therefore irrelevant in our actual situation.
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Kay needs to fix part of her fence.She can buy 6 feet of fencing for $32.00 at a fencing store or 10 feet of fencing for $52.50 at a home store.She visits another store that sells 8 feet of fencing for a certain cost.The cost per foot is between that at the fencing store and the home store.How much the store charge for 8 feet of fencing?
Answer
42.66
Step-by-step explanation:
each foot is 5.33 so 5.33 x 8 is 42.66
What is the predetermined overhead rate? \( \$ 10.00 / \mathrm{MH} \) \( \$ 17.50 / \mathrm{MH} \) \( \$ 20.00 \) / MH \( \$ 32.86 / \mathrm{MH} \)
The predetermined overhead rate is the estimated manufacturing overhead cost per unit of a specific allocation base.
In the options, there are four different rates:
1. $10.00 / MH (MH stands for machine hour): This means that the estimated manufacturing overhead cost per machine hour is $10.00.
2. $17.50 / MH: This indicates that the estimated manufacturing overhead cost per machine hour is $17.50.
3. $20.00 / MH: This implies that the estimated manufacturing overhead cost per machine hour is $20.00.
4. $32.86 / MH: This shows that the estimated manufacturing overhead cost per machine hour is $32.86.
Each rate represents the estimated cost of manufacturing overhead per unit of the allocation base (machine hour) and is used to allocate overhead costs to products or services based on their usage of the allocation base.
The specific rate chosen depends on the nature of the business, its cost structure, and the accuracy of the estimated overhead costs.
The correct question is ''What is the predetermined overhead rate?\(\( \$ 10.00 / \mathrm{MH} \) \( \$ 17.50 / \mathrm{MH} \) \( \$ 20.00 \) / MH \( \$ 32.86 / \mathrm{MH} \)\).''
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How do you find the scale factor of a point dilation?
Answer:
Finding the dilation's center point is the first step in determining the scale factor. Next, we measure the distances between the center point and various points on the preimage and the image. We may determine the scale factor by dividing these distances by 2.
Step-by-step explanation:
A mountain is 18,574 feet above sea level, and a valley is 400 feet below sea level. What is the difference in elevation between the mountain and the valley?
Graphically determine the optimal solution, if it exists, and the optimal value of the objective function of the following linear programming problems. 1. 2. 3. maximize z = x₁ + 2x₂ subject to 2x1 +4x2 ≤6, x₁ + x₂ ≤ 3, x₁20, and x2 ≥ 0. maximize subject to z= X₁ + X₂ x₁-x2 ≤ 3, 2.x₁ -2.x₂ ≥-5, x₁ ≥0, and x₂ ≥ 0. maximize z = 3x₁ +4x₂ subject to x-2x2 ≤2, x₁20, and X2 ≥0.
The maximum value of the objective function z is 19, and it occurs at the point (5, 1).Hence, the optimal solution is (5, 1), and the optimal value of the objective function is 19.
1. Graphically determine the optimal solution, if it exists, and the optimal value of the objective function of the following linear programming problems.
maximize z = x₁ + 2x₂ subject to 2x1 +4x2 ≤6, x₁ + x₂ ≤ 3, x₁20, and x2 ≥ 0.
To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:
Now, To find the optimal solution and the optimal value of the objective function, evaluate the objective function at each corner of the feasible region:(0, 3/4), (0, 0), and (3, 0).
z = x₁ + 2x₂ = (0) + 2(3/4)
= 1.5z = x₁ + 2x₂ = (0) + 2(0) = 0
z = x₁ + 2x₂ = (3) + 2(0) = 3
The maximum value of the objective function z is 3, and it occurs at the point (3, 0).
Hence, the optimal solution is (3, 0), and the optimal value of the objective function is 3.2.
maximize subject to z= X₁ + X₂ x₁-x2 ≤ 3, 2.x₁ -2.x₂ ≥-5, x₁ ≥0, and x₂ ≥ 0.
To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:
To find the optimal solution and the optimal value of the objective function,
evaluate the objective function at each corner of the feasible region:
(0, 0), (3, 0), and (2, 5).
z = x₁ + x₂ = (0) + 0 = 0
z = x₁ + x₂ = (3) + 0 = 3
z = x₁ + x₂ = (2) + 5 = 7
The maximum value of the objective function z is 7, and it occurs at the point (2, 5).
Hence, the optimal solution is (2, 5), and the optimal value of the objective function is 7.3.
maximize z = 3x₁ +4x₂ subject to x-2x2 ≤2, x₁20, and X2 ≥0.
To solve the given linear programming problem, the constraints are plotted on the graph, and the feasible region is identified as shown below:
To find the optimal solution and the optimal value of the objective function, evaluate the objective function at each corner of the feasible region:(0, 1), (2, 0), and (5, 1).
z = 3x₁ + 4x₂ = 3(0) + 4(1) = 4
z = 3x₁ + 4x₂ = 3(2) + 4(0) = 6
z = 3x₁ + 4x₂ = 3(5) + 4(1) = 19
The maximum value of the objective function z is 19, and it occurs at the point (5, 1).Hence, the optimal solution is (5, 1), and the optimal value of the objective function is 19.
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i-Ready
Dilations and Similarity-Instruction-Level H
Figure ABCD is dilated from point Q, the center of dilation.
Which figure is a dilation of figure ABCD?
Figure (c) is a dilation of figure ABCD.
By drawing rays from point Q to each of the vertices of figure ABCD and extending them to intersect with a new figure, we may determine the dilation since figure ABCD is dilated from point Q.
Looking at the possible answers, we can see that only figure (c), with all angles and side lengths proportional to those in ABCD, has the same form as ABCD. Figure (c) shows a dilatation of Figure ABCD as a result.
As figure (c) exceeds ABCD, the dilation has a scale factor higher than 1. In other words, the ratio of the corresponding side lengths is the same for all sides, and each side length and angle in figure (c) are larger than the corresponding side length and angle in ABCD.
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A company offers premium cable for 39.95 per month plus a one time setup fee. The total cost of 6 months of service is 264.70. Write and solve a linear equation to find the total cost for 2 years of service
Answer:
Total cost = 983.8
Step-by-step explanation:
Monthly charge = 39.95
One time set up fee = x
Number of months = y
Total cost = x + 39.95y
The total cost of 6 months of service is 264.70.
264.70 = x + 39.95(6)
264.70 = x + 239.7
264.70 - 239.7 = x
x = 25
Total cost = 25 + 39.95y
Write and solve a linear equation to find the total cost for 2 years of service
2 years = 24 months
Total cost = 25 + 39.95y
= 25 + 39.95(24)
= 25 + 958.8
= 983.8
Total cost = 983.8
Maria is making a rectangular quilt. She starts with a square of fabric with side length x cm.
She adds some fabric to one side of the square and a different amount of fabric to an adiacent side of the square. Her final quilt has an area of x2 + 13x + 30 cm?. How much longer is the long dimension of the quilt than the short dimension?
Therefore, the long dimension of the quilt is (26x + 60)/(x + 6) cm longer than the short dimension.
What is area?Area is the measure of the extent of a 2-dimensional surface or region, usually measured in square units such as square meters (m²), square feet (ft²), or square centimeters (cm²). It is the amount of space inside the boundary of a flat shape or the surface of an object.
Here,
The area of the original square is x^2 cm². Maria adds some fabric to one side of the square, which increases the length of the rectangle by a certain amount, and adds a different amount of fabric to the adjacent side, which increases the width of the rectangle by a certain amount. Let's say Maria adds y cm of fabric to one side and z cm of fabric to the other side. Then the length of the rectangle is x + y cm and the width is x + z cm. The area of the rectangle is given by:
(x + y)(x + z) = x^2 + xy + xz + yz
We know that the area of the rectangle is x² + 13x + 30 cm². So we can set these two expressions equal to each other:
x² + xy + xz + yz = x² + 13x + 30
Simplifying this equation, we get:
xy + xz + yz = 13x + 30
We want to find the difference between the length and the width of the rectangle, which is (x + y) - (x + z) = y - z. To solve for y - z, we need to express yz in terms of y - z. We can do this by factoring the left side of the equation above:
xy + xz + yz = y(x + z) + xz = (y - z)(x + y + z)
Substituting this expression for yz in the equation above, we get:
(y - z)(x + y + z) = 13x + 30
We want to solve for y - z, so let's focus on the left side of the equation:
(y - z)(x + y + z) = y(x + y + z) - z(x + y + z)
= xy + y² + yz - xz - z² - yz
= y² - z² + xy - xz
Substituting the expression we found earlier for xy - xz, we get:
(y - z)(x + y + z) = y² - z² + (y - z)(x + z)
(y - z)[x + y + z - (x + z)] = y² - z²
y - z = (y² - z²)/(y - z) = y + z
= (13x + 30)/(x + 6)
So the difference between the length and the width of the rectangle is:
y - z = (13x + 30)/(x + 6)
Therefore, the long dimension of the quilt is (x + y) = x + (13x + 30)/(x + 6) cm, and the short dimension is (x + z) = x + (30 - 13x)/(x + 6) cm. The difference between the long and short dimensions is:
[x + (13x + 30)/(x + 6)] - [x + (30 - 13x)/(x + 6)]
= (13x + 30)/(x + 6) - (30 - 13x)/(x + 6)
= (26x + 60)/(x + 6)
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coin aa is flipped three times and coin bb is flipped four times. what is the probability that the number of heads obtained from flipping the two fair coins is the same?
P = 35/128 is the probability that the number of heads obtained from flipping the two fair coins is the same.
Describe probability using an example?
By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained. The most basic illustration is a coin toss. There are only two outcomes that can occur when you flip a coin: either heads or tails.P( oH ) = ³C₀ (1/2)³ . ⁴C₀ (1/2)⁴ = 1 . 1/128
P( 1H) = ³C₁ (1/2)³ . ⁴C₁( 1/2 )⁴ = 12/128
P( 2H ) = ³C₂ (1/2)³ . ⁴C₂ (1/2)⁴ = 18/128
P( 3H) = ³C₃ ( 1/2)³ . ⁴C₃ ( 1/2)⁴ = 4/128
P = 1/128 + 12/128 + 18/128 + 4/128
P = 35/128
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Payment option A for leasing new cars is $2,450 down, plus $175 per month for 36 months. Payment option B for leasing new cars is $1,900 down, plus $165 per month for 24 months. How much more would it cost to be on payment plan B for 6 years than payment plan A?
It would cost $1,350 more to be on payment plan B for 6 years than payment plan A.
Payment plan A costs $2,450 down plus $175 per month for 36 months. This is a total of $2,450 + ($175/month * 36 months) = $10,920.
Payment plan B costs $1,900 down plus $165 per month for 24 months. This is a total of $1,900 + ($165/month * 24 months) = $7,640.
The difference between the two payment plans is $10,920 - $7,640 = $3,280.
If you were to pay for 6 years, which is 72 months, on payment plan B, you would pay $7,640 * 2 = $15,280.
The difference between $15,280 and $10,920 is $1,350.
Therefore, it would cost $1,350 more to be on payment plan B for 6 years than payment plan A.
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Find the complex power, the average power, and the reactive power. v (t) = 160 cos (377t) V and i(t) = 12 cos (377t +45) A The complex power is 1-1 VA. The average power is W. The reactive power is VAR
The complex power is 1920 ∠ (-45°) VA, the average power is approximately 1357.1 W, and the reactive power is approximately -1357.1 VAR.
To find the complex power, average power, and reactive power, we need to calculate the complex power S, which is the product of the voltage and current phasors.
Given:
v(t) = 160 cos(377t) V
i(t) = 12 cos(377t + 45) A
The complex power is given by:
S = V * I*
where V is the phasor representing the voltage and I* is the complex conjugate of the phasor representing the current.
In phasor form:
V = 160 ∠ 0° V
I = 12 ∠ 45° A
Taking the complex conjugate of I:
I* = 12 ∠ (-45°) A
Now, we can calculate the complex power:
S = V * I*
S = (160 ∠ 0° V) * (12 ∠ (-45°) A)
Multiplying the magnitudes and adding the angles:
S = (160 * 12) ∠ (0° - 45°) VA
S = 1920 ∠ (-45°) VA
Therefore, the complex power is 1920 ∠ (-45°) VA.
To find the average power, we take the real part of the complex power:
Average Power = Re(S) = Re(1920 ∠ (-45°) VA)
Average Power = 1920 * cos(-45°) W
Average Power ≈ 1357.1 W
The reactive power can be found by taking the imaginary part of the complex power:
Reactive Power = Im(S) = Im(1920 ∠ (-45°) VA)
Reactive Power = 1920 * sin(-45°) VAR
Reactive Power ≈ -1357.1 VAR (Note: The reactive power is negative in this case.)
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Quadrilateral DEFG has coordinates D (2, 1), E (2, 6), F (5, 6), and G (5, 1). How can quadrilateral DEFG be classified?
Group of answer choices
rhombus but not a square
parallelogram but neither a rhombus nor a rectangle
rectangle but not a square
square
Answer:
Rectangle but not a square
Step-by-step explanation:
Let's start by determining if it's a parallelogram.
The slope of side DE is undefined.
The slope of side EF is 0.
The slope of side FG is undefined.
The slope of side DG is 0.
Thia means we have 2 pairs of opposite parallel sides, meaning DEFG is a rhombus.
Now, let's determine if it's a rectangle. Since the slope of
side DE is undefined and the slope of side EF is 0, sides DE and EF are perpendicular. This means that angle DEF is a right angle, and thus DEFG is a rectangle.
To determine if DEFG is a rhombus, we can find the lengths of adjacent sides DE and EF.
The length of DE is 5.
The length of EF is 3.
Since the pair of consecutive sides (sides DE and EF) aren't congruent, DEFG is not a rhombus.
Since DEFG is not a rhombus, it also cannot be a square.
This means DEFG is a rectangle, but not a square.